Theorem bian11da | index | src |

theorem bian11da (G a b c d: wff):
  $ G /\ d -> (a <-> b /\ c) $ >
  $ G -> (a /\ d <-> b /\ (c /\ d)) $;
StepHypRefExpression
1 anass
b /\ c /\ d <-> b /\ (c /\ d)
2 hyp h
G /\ d -> (a <-> b /\ c)
3 2 aneq1da
G -> (a /\ d <-> b /\ c /\ d)
4 1, 3 syl6bb
G -> (a /\ d <-> b /\ (c /\ d))

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)